Polygon Properties: What is Possible? - Article

This article had a lot of information in it about all different types of polygons and geometric shapes. There are three levels of geometric thinking (visual, descriptive, and informal deduction) that are developed and strengthened over the grade school years. Level 0, visual level, the students are stating what a shape is and use nonverbal usage. Students make their discussion and thoughts heard aloud based on what they see and have seen in the past. Level 1, descriptive level, the students will expand on what a shape is and how it is categorized. The example in the article states, "a triangle is no longer a triangle because it looks like one, but because it is a closed figure that has three sides and three angles." This level shows how the students knowledge on the shape and knowledge from the class has helped them. Level 2, informal deduction, students are able to come up with a logical property for why a shape is in the category it is placed in. This was interesting to me, because I never knew that these levels existed. But I like how I they build on each other and promote higher thinking.

One activity that was presented in the article was, Shape Sorting. This activity gave each group of students a bag full of different shapes both regular and irregular. Then the students had to sort them, using any sorting technique they wanted. It gave the students the control in the sorting process. Once they were sorted in the first area, the students would sort them again from the groups they were originally in. I liked how the students each had a different view on what they thought the next sorting area should be. This activity shows so many opportunities to talk about and describe shapes of all kinds.

I liked how with the Shape Sorting activity the teacher made connections to the students about what was happening and what they needed to get done. The students would create their own shape, of any kind, and have to sort it into one of the groups that were created in the activity. They also had to explain why the shape was in this category. (Many process standards were being met in this activity!)

Another activity that was discussed was Riddle Activities which was something new to me, but I found that it was a good way to learn about shapes and shape types. The students were given riddles about a shape and had to determine which shape it could be. The students used Geoboards to show what the shape could be and to show "proof" of an answer. Riddles started out simple and sometimes obvious, but become generally harder and more difficult. The students would use trial and error to determine the shape, and in some cases an answer was not found. Students gradually found out that not every riddle could be solved. I like how this activity has the students working and thinking, even if the riddle is not solved.

Robichaux, R.R. & Rodrigue, P.R. (2010). Polygon properties: What is possible? Teaching children mathematics 16 (9), 524-531.

Manipulative Activities

This was a completely different day, over all the other days we have had in the classroom this semester. Today was the first day where each and every person in class was able to participate in the different manipulative activities that were around the room. I seemed to learn, like each and everyday in class, more about how to properly use and incorporate these different activities to best suit the students.

The one major thing I noticed about doing these different activities is that the teacher would constantly be walking around the room to make sure each student was helping work with the different manipulative. I think it could be hard to determine how to hold every student accountable, so having a check list or just observing the students might be enough. I also think that by having each group member at a manipulative table switch off who was writing down the information was another great idea. This way when the papers are collected, the teacher can see exactly who was writing and see the different handwriting analysis on the paper.

All types of games and activities have to have some kind of catch phrase to attract the buyers to them. But the phrase, "Hands-On" has been eliminated and has been brought back to life with, "Hands-On, Mind-On." I think that the, "Hands-On, Minds-On" is a much better way to promote a product. This way it is an activity that is done with your hands, but at the same time you are thinking of all the possibilities that can come with these activities. For example, the unifix cubes or the snap cubes, those were both hands-on and mind-on. You obviously had to use your hands to figure out different ways to use the cubes, but you also had to use your mind to see how and why certain situations took place. There is more thinking involved when something is mind-on because students not just playing with the manipulative.

The process standards are used in many ways with all the different manipulative activities. Students and teachers will be able to determine different types of reasoning and proofs to try and prove a point about how a manipulative could work. Communication, this will take place all the time, when students are talking to one another about their ideas for how a manipulative could work. There are always many different ways for them to be used. Connections could be made between subjects or lessons being taught, and they could be made about the different types of manipulative activities being used. For example, I was making connections between the unifix cubes and the snap cubes on how they were similar, yet different from one another. Students will be able to problem solve and become more aware of the problem solving when working with hands-on minds-on activities. They allow students to think in a more abstract and out-of-the-box way that can help them develop. Representation, how was this not used in the manipulative activities? Every thing that was taking place with the manipulative activities was being represented in a different way and was able to mean something else at some point.

I really enjoyed doing these activities, I feel like I know more about them and how to use them in the correct way and how to give proper instruction (when it is given) to the students.

Technology Reflection

When didn't we use technology this semester? We have used so much technology everyday this semester, some of which I have never used before. The smart board was the coolest new piece of technology that I used this semester. Smart boards were a lot easier to use than I had anticipated. It was interesting to see all the different things you could do with the smart board. I was happy that I stayed in the classroom a few weeks ago when the other education classroom came in, because I was able to see all the different things that could be done on the smart board, that is not directly related to mathematics. It was cool to see that a smart board could be used with all different students at all different grade levels. There was so much that could be done on the smart board. I thought it was interesting to see that the smart board could use sound effects to say different letters.

Computers, another piece of technology that we used each and everyday. Computers have so many possibilities for teaching and for showing many examples for mathematics. I liked how much work we had to do on the computers. I felt that the way of communication of Google Docs was a little hard at first, but as the semester went on I began to understand it a little more.

Just recently we used calculators, which I have personally used since I was in grade school. But the type of calculator that was used was a little different from what I had back in those days. So these calculators where interesting to see and use. I was hoping that we would see a calculator that would hook up to a computer and see how it is used in that form.

Problem Errors Reflection

I really liked the problem errors that we worked on. I felt that it was good to see how students can come up with different answers to general math questions. I also found it interesting that if a teacher gives too much information about a particular math problem, the students could just be using the wrong rules on the problem. I think that doing this will help me to space out information about a given topic, so students are not overwhelmed with too much information.

I liked how the entire packet of error problems, gave a large perspective of what could happen with a real student. Also the variety of problems that were given also gave me an understanding of what was happening and how to teach the material in a better way. I believe that the packet hit on a lot of math topics, that seem easy and understandable to everyone, but that do have a way of getting confusing. I felt that seeing all these different ways was helpful and gave insight about what to look for as a future teacher.

I think that one element that I would have liked to see throughout the packet, would be how two students interpreted the problems. I know it would make the packet longer, but I believe it would help us in the long term. This way we can see two different ways that a problem was interpreted by the students.

Map Scale, Proportion, and Google Earth

This article dealt with a lot of different elements to the world outside of math, and the world inside of math. This article took the concept of distance and approximation to a whole new level. Students needed to use Google earth and the different formulas and elements learned in math to measure real life images of the world. Students learned many different terms that would relate to the math terms, but also related to the maps that they were looking at. For example, scale was used to show the different ways to weigh objects, but then it is also used to determine the different distances on a map (Google earth images). Students also found it interesting to find their own homes and complete measurements on a familiar location.

I really liked how the students were using Google earth to find the different mathematical elements being studied. I found this to be a great real life situation concept that students could use later on in their lives as well as at the present time. It was interesting to see how the students learned the different forms of the scaling. For example, the students noticed the differences of the inside and outside of a football field. This helped show that measuring and knowing mathematical formulas is beneficial to students understanding of the world.

Roberge, M. & Cooper, L. (2010). Map scale, proportion, and Google earth. Mathematics teaching in the middle school 15(8), 448-457.

A Foxy Loxy and a Lallapalagram - Article

This was a very interesting articles pertaining to how there is a different language in the mathematical world, to the world of other subjects. Many of the students discussed in this article did not have English as a first language, many of them were learning it as a second or third language. So when the teachers would ask for specific information about a particular shape some students would answer in their native language. Students were able to say what a shape was, but were not able to speak about what the shape was mathematically called. For example, students knew square, but when the teacher turned it and held it by a corner, the students called it a diamond. Students were also not able to comprehend what was being explained to them when the teacher was explaining details to them.

I found it extremely interesting in the way that the students explanation of information to the teacher. They would state the different principles that a rectangle had, and the teacher would try and have them elaborate on what they stated. This way the students understood that they needed to use mathematical terms that were descriptive of what was being learned. For example students needed to explain what 'straight' meant and how they could expand on what they are trying to say.

Wilson, J. (2010). A foxy loxy and a lallapalagram. Teaching children mathematics 16(8), 492-499.